Contrast structures in simplest variational vector problem and its asymptotics

摘要

Contrast structures (trajectories with inner and boundary layers) in simplest vector variational problem are stdied. Necessary optimality conditions lead to singularly perturbed vector nonlinear boundary value problems, for which contrast structures were not investigated before. Applying Krotov's functions to these solutions leads to new results: structures of spike type are connected with points of local maximum and structures with inner passages are connected with the points of global maximum of some functional.